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A mathematical model for airfoils with spoilers or split flaps Yeung, William Wai-Hung


A flow model for a Joukowsky airfoil with an inclined spoiler or split flap is constructed based on the early work by Parkinson and Jandali. No restriction is imposed on the airfoil camber, the inclination and length of the spoiler or split flap, and the angle of incidence. The flow is assumed to be steady, two-dimensional, inviscid and incompressible. A sequence of conformal transformations is developed to deform the contour of the airfoil and the spoiler (split flap) onto the circumference of the unit circle over which the flow problem is solved. The partially separated flow region behind these bluff bodies is simulated by superimposing suitable singularities in the transform plane. The trailing edge, the tip of the spoiler (flap) are made critical points in the mappings so that Kutta conditions are satisfied there. The pressures at these critical points are matched to the pressure inside the wake, the only empirical input to the model. Some studies of an additional boundary condition for solving the flow problem were carried out with considerable success. The chordwise pressure distributions and the overall lift force variations are compared with experiments. Good agreement in general is achieved. The model can be extended readily to airfoils of arbitrary profile with the application of the Theodorsen transformation.

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